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28 September 2010

I'm more than a little surprised by this post by Steven Goddard. His answer to my title question is yes. That he's wrong isn't very interesting. We all make mistakes, and particularly so when speaking outside areas that we've studied. The two main physical processes which show his error are interesting in their own right, and I'll take this chance to discuss them -- they are rivers (which say 200 years should be noticeable), and what happens to fresh water at 4 C (which says the memory is 1 year [oops, 6 months]).

First, I'll take a look at a less interesting error that minimal self-checking would have pointed to a difficulty. But that introduces a useful tool -- the 'sanity check'. Namely, he suggests that the reason Lake Superior is still cold is because it's so large that it is still adjusting to the end of the last ice age. That's about 10,000 years ago. Ok, suppose this line of reasoning is true. While Superior is large, is it tiny compared to the oceans. If Superior takes 10,000+ years to adjust, something 10 times bigger should take 100,000+ years to adjust. The ocean is about 100,000 times larger (in volume) than Lake Superior.Goddard's line of reasoning, then, suggests that the ocean's time to react to climate change is over 1,000,000,000 years. This is not a rigorous argument, of course, it's what we call a 'sanity check'. If your argument is true in one area, what happens when you apply it to a different area? Does it still make sense? If the ocean's response time to climate change were a billion years, the present ocean would still not know that we moved towards ice age conditions about 35 million years ago -- it should be warm, as most of climate over this period has been warm.

The sanity check alerts us that there may well be something wrong with the line of reasoning. We still need to look at what kinds of things could be at play to cause the answers to be so unreasonable. Perhaps it's true after all, there being some extra thing going on to make Lake Superior wildly different than the oceans. One process is river inflow, something which affects both the oceans and Great Lakes. Namely, every year, water flows in to Lake Superior, and to the oceans. Water also flows out of Superior (though not the oceans, at least not to speak of). In other words, the water that's in Lake Superior today wasn't there at some time in the past.

What we can do is divide the volume of the oceans, or Superior, by the volume of water flowing in each year. That gives us what is called a 'residence time' -- the period that, if the body mixed up thoroughly every year, it would take to replace all the water that was there when you started. The residence time for Lake Superior is 191 years (same wikipedia link as above), round it to 200. For the ocean, I compute it at 40,000 years by this consideration and some remembered figures. In both cases, then, figures quite a lot faster than was given by Goddard, or inferred by applying his reasoning to the oceans.

Let's look specifically to Superior, now. Does anything happen to mix it up? Well, there are winds, of course. The winds kick up waves, which stir up the upper parts of the lake. If it were true (it isn't) that the river inflow all stayed at the top of the lake, and all flowed out from the tops of the lake, then maybe the deeper waters would remain unaware of more recent climate. (This possibility is why you don't stop with the sanity check, and why you don't stop with the rivers. Keep pushing.)

4 C is the figure to remember. What happens is that fresh water is densest at 4 C (39 F). So let us think about Lake Superior as it heads for winter. At the end of the summer, the water is 'warm'. Meaning just that it's over 4 C, though often not by a whole lot. You can see current conditions at the Great Lakes Environmental Research Lab. As I'm writing, most of the lake is above 50 F (10 C).

As we get in towards winter, the lake will cool. 9 C water is denser than 10 C water, but this warm water (for Superior!) is all near the surface. So a bit of mixing will occur in that near surface layer . Cool some more, to the point that the water is only slightly above 4 C. Not a difficult thing, as northern Minnesota and southern Canada are far colder than that in winter. Mixing occurs deeper, since the water is almost as dense as it can get, but, still, only the upper portion of the lake. Now continue cooling, to the point of the surface water being 4 C. This is the densest you can make fresh water (ocean water is different). The entire water column then overturns all the way to bottom. This thoroughly mixes up the lake, and does so every year that northern Minnesota gets cold.

update: As the lake warms up from its winter cold, the surface warming from near 0 C towards its balmy summer 10 C, the same process happens on reaching 4 C. So every fall and every spring, for as long as winders are cold, the lake overturns. (original) The longest 'memory' Lake Superior, or any cold winter lake, can have is 6 months -- since the last overturning event. Lake Superior certainly does not 'remember' the last ice age. It doesn't even remember the cold winters of the 1970s.

Lake Superior is cold because fresh water is densest at 4 C, and humans think that's a cold temperature for a lake.

The field of science that studies lakes is limnology, so this is a useful term to include in your searches for further information. A nifty process related to this 4 C business is called 'thermal bar'.

23 comments:

Thanks MJB. I missed the spring event. Same thing will happen as we warm the winter's cold water from near 0 C to above 4 C -- on hitting 4, the lake overturns. I just found it easier to think about the fall/winter cooling season. The text is revised.

In like vein of fallibility, my question about references for there being question about whether Superior overturns everywhere, every fall and spring, was serious over at Goddard's. My chatting with 'friends at GLERL' (ok, colleagues) is not a serious citation. It was lunchtime conversation, not professional writing. For such casual conversation, we're not going to be terribly concerned about every i being dotted and t crossed. So it's possible that the debate you mention at Goddard's is also in the professional circles. If you have a reference, or find one, I'll be interested in reading it and making what further updates are needed for this article.

Hmm. Will the overturning necessarily extend all the way to the bottom though? As a parcel of dense 4-degree water sinks, it will warm up (if falling through warmer waters) or cool down (if falling through colder waters). If the thermal transfer is rapid enough, and the lake deep enough, the temperature will equilibrate long before the circulation reaches the bottom of the lake.

I guess there are another couple of sanity-check calculation you can do. Let's assume the entire lake starts at precisely freezing temperature. If the surface temperature is held at 1 degree C, what's the rate of conductive heat transfer at the average depth (100m) and maximum depth (400m). How long would that take to warm the lake purely by conduction? Overturning can only speed this up, not slow it down, so that gives us an upper bound on the lake's "memory".

A quick back of envelope calculation suggests it's around 1000 years, but I may be wildly wrong on that...

Further comment: I disagree with your first sanity check. Yes, the oceans are 100,000 larger in volume than Lake Superior. That doesn't mean they'll take 100,000 as long to respond to the end of the Ice Age.

You could very plausibly make the argument that we only need to care about the depth of the ocean, since we're interested in how well heat makes it from the warm surface to the cold bottom. In that case, the oceans are on average something like 50 times as deep as Lake Superior, and so might be expected to take 50 times as long to respond.

The ocean unfortunately is not just a big lake. You can't model it like one because it is large enough that latitude-driven thermal and salinity differences are the main drivers of most ocean circulation, rather than seasonal change. As such, it probably isn't at all sensible to describe the amount of time it takes for the ocean to mix as a multiple of the amount of time it takes for a lake to mix.

This is why the deep waters of any temperate (or arctic) freshwater lake are always at about 4C. In the winter, and again in the spring, the surface waters reach that temperature and sink. The rest of the time, there's a thermocline.

It's somewhat analogous to the thermohaline circulation in the oceans, which is the reason all the deep ocean waters are high salinity and around 0C. But the details are different because salt water, unlike freshwater, doesn't have a density maximum above freezing.

Interesting comments. Thanks, deech, for the link to a much better Lake Superior page.

Peter:I took the volume-based check because Goddard based his comment on volume. Certainly there are other routes to making a sanity check. But, since he was thinking in terms of volume, he could (should) have checked his statement.

vinny:Indeed, Lake Baikal has about twice the volume of Lake Superior. There are still other errors in Goddard's note and comments. The interesting errors to me were the absence of any sanity check, ignoring rivers, and ignoring the 4 C turnover, so I took those up.

Re: volume v. depthIn the case of thermal conduction the time constant for approach to equilibrium depends on the SQUARE of the linear dimension (depth in this case). So still quite a significant difference between lake and ocean. But other processes are likely to dominate in the ocean.

I'll be honest, I'm not in the least bit surprised when Goddard gets things wrong! All least all these "d'oh" moments will be collected under one handy new URL. Very infomative post too, I must say.

I have an unrelated question that hopefully you can answer: a person on a forum I post on showed a graph of recent RTOFS current speed output (here for interested onlookers) and an archived analysis from 2009. These charts do seem to show that the whole north Atlantic circulation has weakened somewhat over the last year, so in the face of recent "ZOMG Gulf Stream is shutting downz" madness, is this a reliable comparison to make given that runs are only archived for 3 months, and is this variation in the current unusual?

I did have a look at the output from the Mercator model, which is archived for longer, and I will say 2008, 2009 and 2010 all look very similar.

If Superior takes 10,000+ years to adjust, something 10 times bigger should take 100,000+ years to adjust.

I agree with Peter that this was overly simplistic. Surface/volume ratios would be more important. In the most theoretical, least physically informed model, you would consider a sphere with a volume of 10X (V = 4/3 * Pi * r^3), and apply the heat diffusion equation to it.

Previous observations and modeling studies of Lake Superior have only partly elucidated its large-scale circulation, in terms of both the climatological state and interannual variability. We use an eddy resolving, three-dimensional hydrodynamic model to bridge this gap. .... Model results are compared to available direct observations of temperature and currents. ... Surface circulation patterns in winter mimic wind directions, but become organized in summer by the presence of thermal gradients...."..."Long-term trends due to changing meteorological forcing are found. Model results suggest the increase in lake surface temperature (0.37 C/decade) is significantly correlated to increases in wind speed above the lake (0.18 m/s/decade), increased current speeds (0.37 cm/s/decade), and declining ice coverage (-886 km2/yr)."

Regarding the ocean's I have some amateur views that are informed to a degree.

I would challenge any long term "thermal" memory for the ocean (>1000 years).

Why?

Firstly that the ocean is upwelling, for most of the ocean this averages around 4m/year, so in 1000 years the entire body of the water is, on average, brought towards the surface and only rejoins the bottom water at polar ocean temperatures (~2C?). Essentially its memory is wiped clean by internal circulation, you do not have to wait for it to cycle through rainfall etc.

Secondly, as I understand it, the two principle ways for heat to move through the main body is the above described upwelling and coastal upwhelling which do not write much of a signal unless the bottom water production temperature changes, or by diffusion.

Diffusion in its general form was worked out by Munk about 50 years ago. From which he derived a scale height (the effective thermal depth of the ocean) around 1000m. One can also calculate a scale time (although he didn't) which is around 250 years. Basically like the scale height, it is a time constant due to two competive processes downward diffusion and upwelling. Basically diffusion down an up escalator. This limits the amount of the ocean that is "reachable" by downward diffusion.

So for variations that do not involve changes in the temperature at which bottom water is produced there may be a short memory e-folding forgetfulness ~250 years. And for changes in bottom water production temperature around 1000 years, providing the circulation is unchanged.

My limited understanding is that during periods of circulatory collapse, stagnant stratified oceanic conditions, the time constants are much larger, the scale heights and times are no longer valid as they depend on upwelling.

I beleive such periods of stagnation may be part of the ancient oceanic record but don't quote me.

Anyway that is the view of someone who has read a little. Unfortunately so few oceanographers seem to contribute to the climablog.

From the title of the post, I thought this was going to be about land levels rebounding from the weight of the ice. In that sense, at least, i think Lake Superior (or at least the lake bed) does remember the ice age...

dzdt:That's a different sort of memory, and, yes, the Great Lakes, or at least Michigan, Huron, and Superior, do show signs of remembering the last ice age. The reason I name those three in particular is that they have substantial north-south distances. The south end had the weight of the ice sheet removed first and is now rising more slowly than the north. So there's something of a tipping going on. As the north side rises faster (than the south) the water recedes from the north and piles up towards the south. You can see this by looking at 100 year old properties that were beachfront at the time.

Has anyone done a SST comparison on the temperature relationship between areas where upwelling occurs and where none occurs? If the relationship has changed it could be interesting. Would there be enough data to get a proxi for deep ocean temperature change?

This is a better one to follow up at one of the 'question place' notes (August is most recent and still open; I've been under the weather).

But the quick answer is that upwelling is indeed examined, and connected to sea surface temperatures. This is more an issue in the ocean (or I'm more an oceanographer than limnologist), and one of the major examples is the cold tongue of water on the equator extending west from Peru -- ordinarily. El Nino shuts down that upwelling, and then leads to surface warming.

I'll have to think about how deep a proxy it would provide, for how much of the ocean (not very much, but some is better than none).

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About Me

In my day job I work on the oceanography, meteorology, climatology, glaciology end of my science interests, but I'm interested in everything, science or not. So I've also been on stage in a production of Comedy of Errors, run an ultramarathon, and been to Epidaurus, Greece, to see a production of Euripides' Iphigenia among the Taurians
Prior to starting the current job, I was a post-doc in oceanography in the UCAR ocean modelling program, and earned my doctorate from the Department of the Geophysical Sciences at the University of Chicago (1989). My undergraduate degree involved Applied Math, Engineering, Astrophysics, and Glaciology.
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